Chapter A.10, Problem 36AYU

To determine

To find: Simplify the expression ${(\sqrt{x}+\sqrt{5})}^2$.

Answer to Problem 36AYU

The value of ${(\sqrt{x}+\sqrt{5})}^2=x+5-2\sqrt{5}\sqrt{x}$.

Explanation of Solution

Given:

It is asked to find the simplest form of the given expression ${(\sqrt{x}+\sqrt{5})}^2$.

Calculation:

Consider ${(\sqrt{x}+\sqrt{5})}^2$,

$(\sqrt{x}+\sqrt{5}{)}^2=(\sqrt{x}{)}^2+(\sqrt{5}{)}^2-2\sqrt{5}\sqrt{x}$

$=\left|x\right|+\left|5\right|-2\sqrt{5}\sqrt{x}=x+5-2\sqrt{5}\sqrt{x}$